1. Field of the Invention
This invention relates to mass spectrometers and more specifically to electrostatic orbital trap (OT) mass spectrometers (MS), and methods and systems for the detection of ions in mass spectrometers using orbital traps.
2. Description of the Related Art
In a high-performance Fourier transform (FT) mass spectrometer (MS), the mass-specific oscillating motions of the ions in a magnetic and/or electric fields are detected as image currents induced by the ions in detection electrodes. High-performance mass spectrometry is typically understood in the art to be a technique which typically is capable of achieving mass resolving power of at least 20,000 (using a FWHM—full width at half maximum, definition) and mass accuracy of 20 ppm or better. The entire contents of all references cited below are incorporated herein by reference in their entirety.
There are two major classes of the high-performance FTMS instruments distinguished by the use of either magnetic or electric fields for trapping ions. Currently, Fourier transform electrostatic orbital trap mass spectrometers (FT-OTMS) based on the use of a quadro-logarithmic electric field for trapping ions have gained widespread use in various applications, mostly due to 1) the simplicity of the electric field generation (as compared to the generation of strong magnetic fields) and 2) the lower cost of manufacturing.
In cylindrical coordinates (r,φ,z), the ideal quadro-logarithmic electric field potential U(r,z) (sometimes also referred to as a hyper-logarithmic electric field potential) can be described as follows:
                              U          ⁡                      (                          r              ,              z                        )                          =                                            k              2                        ⁡                          [                                                z                  2                                -                                                      r                    2                                    2                                            ]                                +                                    k              2                        ⁢                          R              m              2                        ⁢                          ln              ⁡                              [                                  r                                      R                    m                                                  ]                                              +          C                                    (        1        )            where k is a field strength constant, Rm>0 is a characteristic radius, and C is a potential constant.
The motion of an ion having mass m and electric charge q along the axis z in the trapping quadro-logarithmic field (q·k>0) is a simple harmonic oscillation near the plane z=0:z(t)=Az cos(ωt+θ)  (2)where t is the time, Az and θ are the amplitude and the initial phase of the axial oscillation, respectively, and
                    ω        =                              qk            m                                              (        3        )            is the frequency of axial oscillations.
The ion motion in the polar plane (r,φ) in a general case is a complex elliptical rotation around the z axis which is completely decoupled from the ion axial oscillations. When the ellipse is close to a circle of radius R, the ion rotational frequency ωφ is described as (A. Makarov, Anal. Chem, 2000, v. 72, p. 1156-1162):
                              ω          φ                =                  ω          ⁢                                                    1                2                            ⁡                              [                                                                            (                                                                        R                          m                                                R                                            )                                        2                                    -                  1                                ]                                                                        (        4        )            The ion rotational motion is stable at R<Rm/√{square root over (2)} and is unstable at higher rotational radii. The ion kinetic energy Kφ associated with this rotational motion is independent on mass and can be written as
                              K          φ                =                                            q              k                        4                    ⁢                      (                                          R                m                2                            -                              R                2                                      )                                              (        5        )            
Ion traps based on the quadro-logarithmic electric field potential and its approximations (usually referred to as Kingdon traps) have been known for a long time (see K. H. Kingdon, Phys. Rev., 1923, v. 21, p. 408-418; R. D. Knight, Appl. Phys. Lett., 1981, v. 38, p. 221-222). A. Makarov was the first who showed their capabilities for use in high-performance mass spectrometry (U.S. Pat. No. 5,886,346). Makarov's orbital trap design (also referred to as Orbitrap) is based on the detection of a current induced on trap electrodes by ion's collective axial oscillations in a virtually ideal quadro-logarithmic electric field followed by frequency analysis of the measured signal (usually by Fourier transform method) to obtain mass spectrum. The Orbitrap mass spectrometer has been commercialized by Thermo Fisher Scientific, Inc.
The main features of a standard Orbitrap are shown in FIG. 1. It consists of a split outer barrel-like electrode and a coaxial inner spindle-like electrode that form an electrostatic field with quadro-logarithmic potential distribution. In all the commercial Orbitraps from Thermo Fisher Scientific, Inc., the characteristic radius Rm=22 mm; the maximum inner electrode diameter R1=6-9 mm; the maximum internal radius of the outer electrode R2=15 mm (R2≈Rm/√{square root over (2)} to make the rotational motion of ions stable inside the trap); and the overall length is about 3·R2 or more.
The Orbitrap has a slit (typically 0.1-0.03 mm wide) between outer electrode halves and an injection slot (typically 0.8×5 mm2) in one of the outer electrode halves. The ions are injected as a short bunch (typical bunch duration <1 μs) into the injection slot perpendicularly to the z axis and tangentially to the outer electrode surface with the outer electrodes grounded and the attractive voltage (Vi=−3.5-5 kV for positive ions) applied to the inner electrode.
Electrodes of the Orbitrap mass spectrometer create an electric field that is inhomogeneous in two directions, radial and axial. The radial field Er attracts ions toward the central electrode, this field being stronger near the central electrode. To provide a circular trajectory, the tangential velocity of ions needs to be adjusted to such a value that the centrifugal force compensates the force created by Er. The axial field strength Ez is at zero in the equator plane of the Orbitrap analyzer but increases uniformly in opposing directions along the z axis as the two coaxial electrodes become progressively closer. This means that the axial electric field directs the ions toward the equator of the trap with the force proportional to the distance from the equator. Ions accelerated toward the equator continue to migrate through the equator (point of zero force) along the z axis, but decelerate as they continue toward the opposite end of the Orbitrap expending the axial velocity previously gained in traversing the electric field gradient from the starting point to the equator. Once slowed, the ions are accelerated back toward the equator of the trap by the symmetric electric field along the z axis. In this way, the ions oscillate naturally along the z axis. This oscillation is then combined with a more complicated rotational motion. Due to properties of quadro-logarithmic potential, axial motion is harmonic, i.e. it is completely independent not only of motion around the inner electrode but its frequency is independent also on all initial parameters of ions except their mass-to-charge ratios m/q.
To increase the mass range of the trapped ions, the attractive voltage during ion injection is ramped from about 0.75·Vi to the maximum Vi for 20-100 μs (so called electrodynamic squeezing trapping method). The injected ions do not require any additional excitation to start axial oscillations as the ions are injected away from the equatorial plane z=0 so they start oscillation as a cloud immediately after the injection with an amplitude Az≈7 mm. The ion oscillatory motion is detected by measuring the current induced on two halves of the trap outer electrode. The current is amplified, digitized and frequency-analyzed (typically using Fourier transform method) to obtain the mass spectrum.
According to equations (2) and (3), in the ideal quadro-logarithmic field, ions perform simple harmonic oscillations along the z axis with frequencies that depend on the ion's m/q ratio only which is the basis for ion mass measurement in FT-OTMS with very high mass resolution and accuracy. In practical Orbitrap instruments (as it was indicated by A. Makarov et al. in U.S. Pat. No. 7,714,283), because of slight deviations of the field inside the trap from the ideal quadro-logarithmic potential, these frequencies also slightly depend on the amplitude of the ion axial oscillation.
As a result, the phases of oscillations for separate ions are spread out over the time and the coherent motion of the initially tight ion cloud disappears with time that limits the instrument mass resolution and accuracy. As it was pointed out in U.S. Pat. No. 7,714,283, this problem of loss of coherent motion is due to imperfection of the electric field inside the trap because of limited manufacturing tolerances and non-ideal approximation of the quadro-logarithmic potential by the electrode geometry used. Over time the accuracy of electrode manufacturing improved, and the manufacturing tolerances are presently within a few microns. In addition, many of the mechanical imperfections have diminished due to averaging feature of ion rotational and oscillating motions.